Lesson 2.3

In lesson 2.3, we will be able to find the zeros of polynomial functions, find irrational and complex zeros of polynomial functions, and write polynomial functions.

Steps

1. Use the Rational Zero Theorem to list all possible rational zeros of the function.
2. Use synthetic division to evaluate a given possible zero by synthetically dividing the candidate into the polynomial. If the remainder is 0, the candidate is a zero. If the remainder is not zero, discard the candidate.
3. Repeat step two using the quotient found with synthetic division. If possible, continue until the quotient is a quadratic.
4. Find the zeros of the quadratic function. Two possible methods for solving quadratics are factoring and using the quadratic formula.

Steps

• Write the term with the highest exponent first
• Write the terms with lower exponents in descending order
• Remember that a variable with no exponent has an understood exponent of 1
• A constant term (a number with no variable) always goes last.